## GRE Probability

## Definition

**Probability of event = ****is/of=****(favourable case of the event )/(total number of possible outcomes)**

**Symbolically, P[E] = ****(n[E])/(n[S])**

**independent Event: occurrence of one event does not affect another event.**

**Exp. On certain days having breakfast and raining **

**For independent event P[A and B] = P[A]×P[B]**

**Mutually Exclusive Event: no events are common in **

**two independent events.**

**Multiple of 3 less than 20 = {3, 6, 9, 12, 15, 18}**

**and multiple of 7 less than 20 = {7, 14}**

**But Multiple of 3 less than 25 ={3, 6, 9, 12, 15, 18, 21, 24}**

**and multiple of 7 less than 25 = {7, 14, 21}**

**is not mutually Exclusive Event.**

**For any two independent event **

**P[A or B] = P[A] + P[B] for mutually exclusive event**** **

**= P[A] + P[B] – P[A and B] for a not mutually exclusive event.**

**Probability of not happened = 1 – the probability of happening**

**Probabilities are written as:**

**Fractions from 0 to 1**

**Decimals from 0 to 1**

**A percentage from 0% to 100%**

**The probability of an event always lies between 0 and 1**

**If P = 0 then there is an impossible event**

**If P = 1 then there is a sure event**

**P = 0.5 or ½ equally likely event**

## Example Questions

1. From a list of ten consecutive positive numbers, a number is chosen at random. What is the probability that the number is higher than the average?

** ****(****A) **** ****3/10 ****(****B) **** ****2/5 ****(****C) ½ ****(****D) **** ****7/10 ****(****E) **** ****4/5**

**In the case of even no. of consecutive integer,**

** there is equal no of an integer greater and less than mean.**

**So, P = ****1/2 **

**The answer is C. **

2. What is the probability of selecting a cherry candy from a jar containing two cherry candies, two liquorice candies, and one peppermint candy if you choose one candy at random from the jar?

**P[cherry candy] = ****(****cherry candy)/total**** = ****2/(5 )**

**Answer is D.**

3. There are twice as many red marbles as blue marbles in a bag of marbles, and twice as many blue marbles as green marbles. What is the probability of randomly selecting a blue marble from the bag if these are the only colours of marbles in the bag?

**(****A) **** ****1/6 ****(****B) **** ****2/9 ****(****C) **** ****1/4 ****(****D) **** ****2/7 ****(****E) **** ****1/3**

**Let green marble = 1 **

**Blue marble = 2**

**Red marble = 4**

**P[blue marble] = ****2/7**

**Answer is D.**

4. The integers 1 to 100 inclusive are labeled on the tiles; no numbers are repeated. What is the probability that the product of the two integer values on the tiles is odd if Alma chooses one tile at random, replaces it in the group, and then chooses another tile at random?

**(****A) **** ****1/8 ****(****B) **** ****1/4 ****(****C) **** ****1/3 ****(****D) **** ****1/2 ****(****E) **** ****3/4**

**P[odd and odd] = ****50/100**** ×****50/100** **= ****1/4 **

**Answer is B**

5. One dozen pastries are contained in a box. There are four chocolate pastries, four glazed pastries, and four jelly pastries. What is the probability that two pastries are randomly selected from the box, one after the other, will be jelly pastries?

**Successive Probability**

**P[jelly and jelly] = ****4/12****×****3/11**** = =1/11 **

**[without replacement in question is not mentions**

** however, question sense without replacement ]**

**The answer is A.**